scholarly journals Optimization of gratings in a diffractive waveguide using relative-direction-cosine diagrams

2021 ◽  
Author(s):  
Deqing Kong ◽  
Zheng Zhao ◽  
Xiaogang Shi ◽  
Xiaojun Li ◽  
Bingjie Wang ◽  
...  
Keyword(s):  
Direction Cosine ◽  
Relative Direction

Kinematic Coordination in Human Gait: Relation to Mechanical Energy Cost

1998 ◽  
Vol 79 (4) ◽  
pp. 2155-2170 ◽  
Author(s):  
L. Bianchi ◽  
D. Angelini ◽  
G. P. Orani ◽  
F. Lacquaniti
Keyword(s):  
Energy Expenditure ◽  
Energy Cost ◽  
Time Course ◽  
Sagittal Plane ◽  
Dimensional Space ◽  
Mechanical Energy ◽  
Direction Cosine ◽  
Lower Limbs ◽  
Human Gait ◽  
Plane Orientation

Bianchi, L., D. Angelini, G. P. Orani, and F. Lacquaniti. Kinematic coordination in human gait: relation to mechanical energy cost. J. Neurophysiol. 79: 2155–2170, 1998. Twenty-four subjects walked at different, freely chosen speeds ( V) ranging from 0.4 to 2.6 m s−1, while the motion and the ground reaction forces were recorded in three-dimensional space. We considered the time course of the changes of the angles of elevation of the trunk, pelvis, thigh, shank, and foot in the sagittal plane. These angles specify the orientation of each segment with respect to the vertical and to the direction of forward progression. The changes of the trunk and pelvis angles are of limited amplitude and reflect the dynamics of both right and left lower limbs. The changes of the thigh, shank, and foot elevation are ample, and they are coupled tightly among each other. When these angles are plotted one versus the others, they describe regular loops constrained on a plane. The plane of angular covariation rotates, slightly but systematically, along the long axis of the gait loop with increasing V. The rotation, quantified by the change of the direction cosine of the normal to the plane with the thigh axis ( u 3 t ), is related to a progressive phase shift between the foot elevation and the shank elevation with increasing V. As a next step in the analysis, we computed the mass-specific mean absolute power ( P u ) to obtain a global estimate of the rate at which mechanical work is performed during the gait cycle. When plotted on logarithmic coordinates, P u increases linearly with V. The slope of this relationship varies considerably across subjects, spanning a threefold range. We found that, at any given V > 1 m s−1, the value of the plane orientation ( u 3 t ) is correlated with the corresponding value of the net mechanical power ( P u ). On the average, the progressive rotation of the plane with increasing V is associated with a reduction of the increment of P u that would occur if u 3 t remained constant at the value characteristic of low V. The specific orientation of the plane at any given speed is not the same in all subjects, but there is an orderly shift of the plane orientation that correlates with the net power expended by each subject. In general, smaller values of u 3 t tend to be associated with smaller values of P u and vice versa. We conclude that the parametric tuning of the plane of angular covariation is a reliable predictor of the mechanical energy expenditure of each subject and could be used by the nervous system for limiting the overall energy expenditure.

scholarly journals A DCM Based Attitude Estimation Algorithm for Low-Cost MEMS IMUs

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Heikki Hyyti ◽  
Arto Visala
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Low Cost ◽  
Direction Cosine ◽  
Estimation Algorithm ◽  
Calibration Method ◽  
Attitude Estimation ◽  
Mems Sensors ◽  
Acceleration Sensors ◽  
Adaptive Extended Kalman Filter

An attitude estimation algorithm is developed using an adaptive extended Kalman filter for low-cost microelectromechanical-system (MEMS) triaxial accelerometers and gyroscopes, that is, inertial measurement units (IMUs). Although these MEMS sensors are relatively cheap, they give more inaccurate measurements than conventional high-quality gyroscopes and accelerometers. To be able to use these low-cost MEMS sensors with precision in all situations, a novel attitude estimation algorithm is proposed for fusing triaxial gyroscope and accelerometer measurements. An extended Kalman filter is implemented to estimate attitude in direction cosine matrix (DCM) formation and to calibrate gyroscope biases online. We use a variable measurement covariance for acceleration measurements to ensure robustness against temporary nongravitational accelerations, which usually induce errors when estimating attitude with ordinary algorithms. The proposed algorithm enables accurate gyroscope online calibration by using only a triaxial gyroscope and accelerometer. It outperforms comparable state-of-the-art algorithms in those cases when there are either biases in the gyroscope measurements or large temporary nongravitational accelerations present. A low-cost, temperature-based calibration method is also discussed for initially calibrating gyroscope and acceleration sensors. An open source implementation of the algorithm is also available.

Attitude reconstruction from strap-down rate gyros using power series

2021 ◽  
pp. 1-19
Author(s):  
Habib Ghanbarpourasl
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Direction Cosine ◽  
Analytical Description ◽  
Double Precision ◽  
Angular Velocity Vector ◽  
Higher Order Terms ◽  
Direction Cosine Matrix ◽  
The Stability ◽  
Better Than

Abstract This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

Notes on Screw Product Operations in the Formulations of Successive Finite Displacements

1994 ◽  
Author(s):  
Chintien Huang
Keyword(s):  
Scalar Product ◽  
Direction Cosine ◽  
Linear Representation ◽  
Finite Displacements

Abstract Geometrical interpretations of two line-based formulations of successive finite displacements in terms of screw product operations is discussed. The pitch of the screw product of two unit line vectors is shown to be the ratio of the distance to the tangent of the projected angle between the two lines. Finite twists in Dimentberg’s formulation are interpreted as the screw product of unit line vectors divided by the scalar product of the same unit line vectors. Finite twists in the linear representation are the screw product of unit line vectors divided by the scalar product of the direction-cosine vectors of the same lines.

Relative Direction: Location Path Providing Method for Allied Intelligent Agent

2018 ◽  
pp. 381-391 ◽  
Author(s):  
S. Rayhan Kabir ◽  
Mirza Mohtashim Alam ◽  
Shaikh Muhammad Allayear ◽  
Md Tahsir Ahmed Munna ◽  
Syeda Sumbul Hossain ◽  
...  
Keyword(s):  
Intelligent Agent ◽  
Relative Direction

A New Airborne Passive DF Method only Based on Frequency Difference

2011 ◽  
Vol 219-220 ◽  
pp. 846-850
Author(s):  
Tao Yu
Keyword(s):  
Direction Cosine ◽  
Doppler Frequency ◽  
Frequency Measurement ◽  
Frequency Difference ◽  
Baseline Length ◽  
Direct Proportion ◽  
Unknown Parameters ◽  
Flight Direction ◽  
Phase Interference ◽  
Circular Functions

If three antenna units are divided into two set and two baselines are placed at right angles to each other in flight plain, in which the direction of one baseline is parallel to the actual flight direction of air vehicle, the sine and cosine function of target bearing respectively in two baseline directions can be simultaneously obtained according to the analysis principle of the direction cosine change rate. The angulations’ formula only based on Doppler frequency difference can be derived after eliminating the unknown parameters including angular velocity and wavelength by the specific value of two circular functions. The analog calculation shows that the relative error is in direct proportion to the baseline length provided that the incident wave is parallel in derivation. But the error analysis depicts that the measurement accuracy is in direct proportion to the baseline length. Moreover, the measurement error relies on mainly the accuracy of frequency measurement. Furthermore, the derived formula has irregularity in airborne axis direction. However, since the new method is not associated with wavelength, this new DF only based on Doppler frequency difference will be more adapted to passive sounding as compared with phase interference method.

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